拓扑递归的锥间隙定理
Conifold Gap Theorem for Topological Recursion
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中文总结 AI 辅助
该研究证明了环面对称曲线拓扑递归的锥间隙定理，确定锥极化自由能的通用极项及余项的全纯性，涵盖两类节点并支持更广泛的族形变。
中文摘要 AI 辅助
我们证明了环面对称曲线拓扑递归的锥间隙定理：对于每一个具有普通单节点退化的局部解析族，以及每一个固定的至少为2的亏格，锥极化自由能存在一个通用的极项，其余项在横向参数与旁观参数中联合全纯。该结果涵盖分离与非分离节点，且允许超越纯填充分数情形的一般族形变。
英文摘要
We prove a conifold gap theorem for the topological recursion of toric mirror curves: for every local analytic family acquiring a generic one-node degeneration and every fixed genus at least two, the conifold-polarized free energy has one universal polar term, and the remainder is jointly holomorphic in the transverse and spectator parameters. The result covers separating and nonseparating nodes and allows general family deformations beyond the pure filling-fraction case.
